Ryo Ikehata

Last Updated :2020/12/01

Affiliations, Positions
Graduate School of Humanities and Social Sciences, Professor
E-mail
ikehatarhiroshima-u.ac.jp

Basic Information

Academic Degrees

  • Doctor of Science, Tokyo University of Science
  • Master of Science, Tokyo University of Science

Research Fields

  • Mathematical and physical sciences;Mathematics;Mathematical analysis

Research Keywords

  • wave equation
  • Asymptotic profile, Energy decay
  • Exterior problem, Cauchy problem
  • Fourier Analysis, Real Analysis, Functional Analysis

Affiliated Academic Societies

  • Mathematical Society of Japan, 1988/10

Educational Activity

Course in Charge

  1. 2020, Liberal Arts Education Program1, 1Term, CalculusI
  2. 2020, Undergraduate Education, 2Term, Introduction to Analysis
  3. 2020, Undergraduate Education, 4Term, Practics in Introduction to Algebra
  4. 2020, Undergraduate Education, 4Term, Research Methods in Analysis II
  5. 2020, Undergraduate Education, 4Term, Study of Instructional Materials in Analysis
  6. 2020, Undergraduate Education, Second Semester, Graduation Thesis
  7. 2020, Undergraduate Education, First Semester, Study of Instructional Materials in Analysis Education
  8. 2020, Undergraduate Education, Second Semester, Practical Seminar for the Teaching Profession
  9. 2020, Graduate Education (Doctoral Program) , 1Term, Research into Curriculum and Instruction Sciences (Specialization in Mathematics Education)
  10. 2020, Graduate Education (Doctoral Program) , 3Term, Research into Curriculum and Instruction Sciences (Specialization in Mathematics Education)
  11. 2020, Graduate Education (Master's Program) , First Semester, Project for Integrating Curriculum and Instruction Sciences
  12. 2020, Graduate Education (Doctoral Program) , Second Semester, Special Study
  13. 2020, Graduate Education (Master's Program) , First Semester, Special Study in Mathematics Education A
  14. 2020, Graduate Education (Master's Program) , Second Semester, Special Study in Mathematics Education A
  15. 2020, Graduate Education (Master's Program) , 2Term, Basic Course in Teaching Material Design for Science and Culture(Mathematics) a
  16. 2020, Graduate Education (Doctoral Program) , First Semester, Special Study

Research Activities

Academic Papers

  1. ★, ENERGY DECAY ESTIMATES FOR WAVE EQUATIONS WITH A FRACTIONAL DAMPING, DIFFERENTIAL AND INTEGRAL EQUATIONS, 25(9-10), 939-956, 2012
  2. ★, Optimal decay rate of the energy for wave equations with critical potential, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 65(1), 183-236, 201301
  3. On the existence of global solutions for some nonlinear hyperbolic equations with Neumann conditions, TRU Mathematics, 24, 1-17, 19880401
  4. Yosida approximation and nonlinear hyperbolic equation (with N.Okazawa), Nonlinear Analysis TMA, 15, 479-495, 19900401
  5. On solutions to some quasilinear hyperbolic equations with nonlinear inhomogeneous terms, Nonlinear Analysis TMA, 17, 181-203, 19910401
  6. A class of second order quasilinear evolution equations, 785, 95-111, 19920401
  7. A class of second order quasilinear evolution equations (with N.Okazawa), J. Differential Equations., 114(1), 106-131, 19940401
  8. A note on the global solvability of solutions to some nonlinear wave equations with dissipative terms, Differential and Integral Equations, 8(3), 607-616, 19950401
  9. Stable and unstable sets for evolution equations of parabolic and hyperbolic type (with T.Suzuki), Hiroshima Math. J., 26(3), 475-491, 19960401
  10. On global solutions and energy decay for the wave equations of Kirchhoff type with nonlinear damping terms (with T.Matsuyama), J. Math. Anal. Appl., 204, 729-753, 19960401
  11. Energy decay for the wave equations of Kirchhoff type with linear damping terms (with T.Matsuyama), Math. Japon., 45(2), 315-335, 19970401
  12. The global behavior of weak solutions to some nonlinear wave equations, Gakuto International Series, Math. Sci. Appl. Nonlinear Wavers, 10, 163-168, 19970401
  13. Finite and Infinite Time Blowup of Solutions to Some Semilinear Parabolic Equations, 1061, 43-50, 19980401
  14. The Palais-Smale Condition for some semilinear parabolic Equations, 1123, 76-82, 20000401
  15. Semilinear parabolic equations involving critical Sobolev exponent : local and asymptotic behavior of solutions (with T.Suzuki), Differential and Integral Equations, 13, 869-901, 20000401
  16. Remarks on the decay rate for the energy of the dissipative linear wave equations in exterior domains (with A.Saeki), SUT J. Math., 36(2), 267-277, 20000401
  17. Remalks on the behaviour of solutions to the linear wave equations in unbounded domains (with T.Matsuyama), Proc. School Sci. Tokai University, 36(1), 1-13, 20010401
  18. The Palais-Smale Condition for the energy of some semilinear parabolic equations, Hiroshima Math. J., 30, 117-127, 20000401
  19. Global solutions to the initial-boundary value problem for the quasilinear visco-elastic wave equations with a perturbation (with T.Matsuyama and M.Nakao), Funkcial. Ekvac., 40, 293-312, 19970401
  20. ★, Some remarks on the wave equations with nonlinear damping and source terms, Nonlinear Analysis TMA, 27, 1165-1175, 19960401
  21. L^{2}-behaviour of solutions to the linear heat and wave equations in an exterior domain (with T.Matsuyama), Sci. Math. Japon., 55, 33-42, 20020401
  22. Energy decay of solutions for the semilinear dissipative wave equations in an exterior domain, Funkcial. Ekvac., 44, 487-499, 20010401
  23. Small data global existence of solutions for dissipative wave equations in an exterior domain, Funkcial. Ekvac., 45, 259-269, 20020401
  24. Decay estimates by moments and masses of initial data for linear damped wave equations, International J. Pure Appl. Math., 5, 77-94, 20030401
  25. A remark on a critical exponent for the semilinear dissipative wave equation in the one dimensional half space, Differential and Integral Equations, 16, 727-736, 20030401
  26. Recent progress for dissipative wave equations in unbounded domains, Seminar Notes of Mathematical Sciences, Ibaraki University (Soga H. et al. eds.), 5, 12-25, 20020201
  27. Recent development of a damped wave equation in unbounded domain, Seminar Notes of Mathematical Sciences, Ibaraki University (Soga H. et al. eds.), 6, 51-58, 20030201
  28. Some remarks on the wave equation with potential type damping coefficients, International J. Pure Appl. Math., 21(1), 19-24, 20050401
  29. ★, Local energy decay for linear wave equations with initial data decaying slowly near infinity (with K. Nishihara), Gakuto International Series, Math. Sci. Appl., The 5th East Asia PDE Conference, 22, 265-275, 20050301
  30. Local energy decay for some hyperbolic equations with initial data decaying slowly near infinity (with G. Sobukawa)., Hokkaido Mathematical Journal, 36(1), 53-71, 20070401
  31. Decay estimates of solutions for the wave equations with strong damping terms in unbounded domains, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 24(9), 659-670, 200106
  32. Remark on the L-2 estimates of the density for the compressible Navier-Stokes flow in R-3, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 47(4), 2519-2526, 200108
  33. Critical exponents for semilinear dissipative wave equations in R-N, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 269(1), 87-97, 20020501
  34. Diffusion phenomenon for linear dissipative wave equations in an exterior domain, JOURNAL OF DIFFERENTIAL EQUATIONS, 186(2), 633-651, 20021210
  35. ★, Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain, JOURNAL OF DIFFERENTIAL EQUATIONS, 188(2), 390-405, 20030301
  36. Improved decay rates for solutions to one-dimensional linear and semilinear dissipative wave equations in all space, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 277(2), 555-570, 20030115
  37. L-2-convergence results for linear dissipative wave equations in unbounded domains, ASYMPTOTIC ANALYSIS, 36(1), 63-74, 200310
  38. Diffusion phenomenon for second order linear evolution equations, STUDIA MATHEMATICA, 158(2), 153-161, 2003
  39. Critical exponent for semilinear damped wave equations in the N-dimensional half space, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 288(2), 803-818, 20031215
  40. Local energy decay for linear wave equations with variable coefficients, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 306(1), 330-348, 20050601
  41. Local Energy Decay for Linear Wave Equations with Localized Dissipation, FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 48(3), 351-366, 200512
  42. Global existence of solutions for semilinear damped wave equation in 2-D exterior domain, JOURNAL OF DIFFERENTIAL EQUATIONS, 200(1), 53-68, 20040601
  43. ★, Decay estimates of solutions for dissipative wave equations in R-N with lower power nonlinearities, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 56(2), 365-373, 200404
  44. New decay estimates for linear damped wave equations and its application to nonlinear problem, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 27(8), 865-889, 20040525
  45. Local energy decay for linear wave equations with non-compactly supported initial data, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 27(16), 1881-1892, 20041110
  46. Two dimensional exterior mixed problem for semilinear damped wave equations, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 301(2), 366-377, 20050115
  47. ★, Global existence of solutions for semilinear damped wave equations in R-N with noncompactly supported initial data, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 61(7), 1189-1208, 20050615
  48. Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption, JOURNAL OF DIFFERENTIAL EQUATIONS, 226(1), 1-29, 20060701
  49. Global existence of solutions for 2-D semilinear wave equations with dissipation localized near infinity in an exterior domain, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 29(4), 479-496, 20060310
  50. Decay of solutions for a semilinear system of elastic waves in an exterior domain with damping near infinity, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 67(2), 398-429, 20070715
  51. Global existence of weak solutions for two-dimensional semilinear wave equations with strong damping in an exterior domain, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 68(1), 154-169, 20080101
  52. Total energy decay for semilinear wave equations with a critical potential type of damping, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 69(4), 1396-1401, 20080815
  53. Critical Exponent for Semilinear Wave Equations with Space-Dependent Potential, FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 52(3), 411-435, 200912
  54. Local energy decay for a class of hyperbolic equations with constant coefficients near infinity, MATHEMATISCHE NACHRICHTEN, 283(5), 636-647, 201005
  55. Semi linear parabolic equation in R-N associated with critical Sobolev exponent, ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 27(3), 877-900, 2010
  56. Energy decay rates of elastic waves in unbounded domain with potential type of damping, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 380(1), 46-56, 20110801
  57. ★, Wave equations with strong damping in Hilbert spaces, JOURNAL OF DIFFERENTIAL EQUATIONS, 254(8), 3352-3368, 20130415
  58. Sharp decay rates for wave equations with a fractional damping via new method in the Fourier space, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 408(1), 247-255, 20131201
  59. NEW DECAY RATES FOR A PROBLEM OF PLATE DYNAMICS WITH FRACTIONAL DAMPING, JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 10(3), 563-575, 201309
  60. Optimal decay rates for the system of elastic waves in R-n with structural damping, JOURNAL OF EVOLUTION EQUATIONS, 14(1), 197-210, 201403
  61. ★, Asymptotic profiles for wave equations with strong damping, JOURNAL OF DIFFERENTIAL EQUATIONS, 257(6), 2159-2177, 20140915
  62. ★, Some remarks on the asymptotic profiles of solutions for strongly damped wave equations on the 1-D half space, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 421(1), 905-916, 20150101
  63. Asymptotic behavior for abstract evolution differential equations of second order, JOURNAL OF DIFFERENTIAL EQUATIONS, 259(10), 5017-5039, 20151115
  64. ASYMPTOTIC PROFILES FOR A STRONGLY DAMPED PLATE EQUATION WITH LOWER ORDER PERTURBATION, COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 14(5), 1759-1780, 201509
  65. Fast energy decay for wave equations with variable damping coefficients in the 1-D half line, Differential and Integral Equations, 29(5,6), 421-440, 2016
  66. Optimal decay rates and asymptotic profile for the plate equation with structural damping, J. Math. Analysis and Applications, 440, 529-560, 20160323
  67. ★, Asymptotic profile of solutions for wave equations with frictional and viscoelastic damping terms, Asymptotic Analysis, 98(1-2), 59-77, 2016
  68. FAST ENERGY DECAY FOR WAVE EQUATIONS WITH VARIABLE DAMPING COEFFICIENTS IN THE 1-D HALF LINE, DIFFERENTIAL AND INTEGRAL EQUATIONS, 29(5-6), 421-440, 2016
  69. Critical exponent for nonlinear wave equations with frictional and viscoelastic damping terms, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 148, 228-253, 201701
  70. REMARKS ON LARGE TIME BEHAVIOR OF THE L-2-NORM OF SOLUTIONS TO STRONGLY DAMPED WAVE EQUATIONS, DIFFERENTIAL AND INTEGRAL EQUATIONS, 30(7-8), 505-520, 2017
  71. Remarks on the Decay Rate of the Energy for Damped Modified Boussinesq-Beam Equations on the 1-D Half Line, FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 60(2), 239-257, 201708
  72. Fast energy decay for wave equations with a localized damping in the n-D half space, Asymptotic Analysis, 103(1-2), 77-94, 2017
  73. ★, Asymptotic profile of solutions for some wave equations with very strong structural damping, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 41(13), 5074-5090, 20180915
  74. Asymptotic profile of solutions for strongly damped Klein-Gordon equations, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 42(7), 2287-2301, 20190515
  75. Asymptotic Profiles of Solutions for Structural Damped Wave Equations, JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 31(1), 537-571, 201903
  76. OPTIMAL ENERGY DECAY RATES FOR SOME WAVE EQUATIONS WITH DOUBLE DAMPING TERMS, EVOLUTION EQUATIONS AND CONTROL THEORY, 8(4), 825-846, 201912
  77. Note on asymptotic profile of solutions to the linearized compressible Navier-Stokes flow, HOKKAIDO MATHEMATICAL JOURNAL, 48(2), 357-383, 201906
  78. Moment conditions and lower bounds in expanding solutions of wave equations with double damping terms, ASYMPTOTIC ANALYSIS, 114(1-2), 19-36, 2019
  79. LARGE TIME BEHAVIOR OF GLOBAL SOLUTIONS TO NONLINEAR WAVE EQUATIONS WITH FRICTIONAL AND VISCOELASTIC DAMPING TERMS, OSAKA JOURNAL OF MATHEMATICS, 56(4), 807-830, 201910
  80. Critical exponent for semi-linear wave equations with double damping terms in exterior domains, NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 26(6), 201912
  81. Some remarks on the local energy decay for wave equations in the whole space, Azerbaijan J. Mathematics, 9(2), 167-182, 2019, July
  82. A note on decay rates of the local energy for wave equations with Lipschitz wavespeeds, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 483(2), 20200315

Invited Lecture, Oral Presentation, Poster Presentation

  1. Asymptotic profiles for wave equation with strong damping., Ryo Ikehata, With Invitation, Japanese
  2. Asymptotic profiles for wave equation with strong damping., 2015/12/11, With Invitation, Japanese, other
  3. Fast energy decay for wave equations with a localized damping in the n-D half space, Ryo IKEHATA, Seminar on Partial Differential Equations at UFSC, Brasil, 2016/12/16, With Invitation, English, Federal University of Santa Catarina, Department of Mathematics, Federal University of Santa Catarina, Florianopolis, Brazil, other

External Funds

Acceptance Results of Competitive Funds

  1. KAKENHI, 2015, 2019
  2. KAKENHI, Energy decay for hyperbolic partial differential equations with variable coefficients and its related topic, 2010, 2013
  3. KAKENHI, 2010, 2014
  4. KAKENHI, Energy estimates for hyperbolic equations in unbounded domains and their applications, 2007, 2009
  5. KAKENHI, A study on asymptotic behavior of solutions for evolution equations, 2002, 2004
  6. KAKENHI, 1998, 1999